Topic 3 Essay APT

7/30/2019 Topic 3 Essay APT

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FINANCIAL ECONOMICS PRESENTATION ESSAY:

GROUP 3

TOPIC 3: THE ARBITRAGE PRICING MODEL

STRUCTURE

Arbitrage pricing theory: what is it ? How does it differ from the CAPM? Which is the more appropriate of the model? Which is more practical to use?

APT: WHAT IS IT?

Arbitrage pricing theory is a new and different approach to determining asset prices. It is based

on the law of one price: two items that are the same cant sell at different prices . Unlike CAPM

(one factor model) the ATP is a multi-index/factor model. The primary contribution of the APT

is explaining how one goes from the multi-index model to an economic equilibrium.

Assumptions underlying the APT include:

1. Capital markets are perfectly competitive ( no transaction costs)2. Investors always prefer more wealth to less wealth with certainty (homogenous

expectations)

3. Assumes there is a stochastic process generating asset returns4. APT assumes a multi-factor model of asset returns


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The APT equation is as follows:

= return on asset iduring a specified time period

=expected return for asset I

= reaction/sensitivity in asset is returns to movements in a common factor

=a common factor with a zero mean that influences the returns on all assets

= a random error term with a mean of zero and a variance

This equation is analogous to the next equation.

= the expected return on an asset with zero systematic risk. This means it is not sensitive to

shocks.

ijijiiii IbIbIbaR ...2211

iJJiiibbba ...

22110

0

j

jI

i 2

ei


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The APT model also states that the risk premium of a stock depends on two factors: The risk premiums associated with each of the included factors; and The stocks sensitivity to each of the factors.

If the expected risk premium on a stock were lower than the calculated risk premium in terms of

the formula, the investor will sell the stock. If the expected risk premium were higher than the

value, then investors would buy stocks until both sides of the equation were in balance. Arbitrage

is the term used to describe how investors could go about getting this formula.

DIFFERENCES BETWEEN THE CAPM AND APT

The main difference between APT and CAPM is that the CAPM approach uses a single non-

company factor and a single beta, whereas arbitrage pricing theory separates out non-company

factors into as many as proves necessary. Each of these requires a separate beta. The beta of each

factor is the sensitivity of the price of the security to that factor.

Arbitrage pricing theory does not rely on measuring the performance of the market. Instead,

APT directly relates the price of the security to the fundamental factors driving it. The problem

with this is that the theory in itself provides no indication of what these factors are, so they need

to be empirically determined

APT is also more recent and uses a different approach to determining the asset prices. APT is a

more general approach to asset pricing than CAPM which takes into account mean and variance

iJJiii bbbRmRiskpremiu )(...)()()( 02021010


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of asset returns, while APT instead employs various systematic risk functions to determine asset

price risk and return.

APT also does not rely on as many assumptions as CAPM as the design of the equation allows it

to assess risk and return without them.

WHICH IS THE MOST APPROPRIATE MODEL

A lot of empirical work has been done comparing the APT and CAPM to test which one is the

better model. Most of the findings suggest that APT is a better model than the CAPM, such

findings extend to emerging markets as well (Muzir et al, 2010: 10). However there are few

studies which show that the CAPM is a better model than the APT. Muzir et al(2010: 11) did a

study on the Istanbul stock exchange to compare the APT and CAPM models on their ability to

predict asset returns during periods of economic crises and also comparing the performance of

the two models with each other. Their sample data consists of monthly rates of return on stocks

of 45 listed companies on the Istanbul stock exchange and ranges from January 1996 to

December 2004.

Muzit et al (2010: 15) test the hypothesis in their paper that the APT is more accurate thanCAPM. Their results suggest that the APT is more accurate than CAPM in predicting stock

returns when considering R2 statistics. They reach the conclusion that the APT has a higher

degree of explanatory power than CAPM. Their results on the informative role of both models

during economic crises seem to suggest that APT is more superior than CAPM. The results

suggest that APT outperforms CAPM in reflecting the effects of economic crisis on return

variation.

Dhankar and Singh (2005: 14) also show that the APT is a better model than CAPM inpredicting stock returns in the Indian stock exchange on weekly and monthly return data.

A test that was aimed at contrasting the two models APT and CAPM was carried out by Haugen

(2000). The aim of this paper was to investigate which between these two models was the best

predictor of returns on assets. The period that they looked at was between 1980 and 1999 in

which they analysed stocks of the largest 3500 companies in the United States. Haugen (200)

regressed stock returns against the Standard & Poors 500 which is a free-float capitalization-


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weighted index and recalculated betas each month, betas were used to rank the stocks and were

divided into deciles. This was done in the estimation of the CAPM. In the Implementation of the

APT model six macroeconomics factors were used which were:

1. The monthly return on Treasury bills

2. The difference in the monthly return on long- and short- term Treasury bills

3. The difference in the monthly return on the Treasury bonds and low-grade corporate bonds

of the same maturity

4. The monthly change in the consumer price index

5. The monthly change in industrial production6. The beginning-of-month dividend-to-price ratio for the S&P 500

These six factors were regressed against returns on stocks in the construction of the APT model.

The conclusion of the paper by Haugen (2000) was that APT model was found to predict the

return on assets better than the CAPM.

Lastly a paper by Singh (2008) was analysed. This paper by Singh (2008) compared CAPM and

APT using macro economic variables to represent the APT factors. Singh (2008) analysed 158

Stocks listed on the Bombay stock exchange from 1991-2002. The returns were regressed on

each of the macroeconomic factor separately. In his paper Singh (2008) concluded that that the

APT using principal components analysis was able to explain the cross section of returns much

better than the CAPM. However the factors did not have an economic interpretation. The

macroeconomic factors used in this study were able to explain returns marginally better than

beta alone. While this confirms that risk is multidimensional and that one should not depend on

beta alone, Singh (2008) advocated for further research to identify other variables that can help

explain the cross section of returns.

WHICH IS THE MORE PRACTICAL TO USE

The article that we use is A multifactor approach of APT versus CAPM for the Greek stock

market by Grigoris (2007).


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The purpose of this article is to examine if these models work for the Greek stock market.

Tests of these equilibrium models are important since they influence how the market is viewed.

If either is correct, then that gives a direct influence upon how investment decisions are made

and evaluated. For instance, if CAPM is true then its unnecessary to purchase anything but the

market portfolio.

Sample and Data Selection

The data set consists of 100 stocks traded continuously on the Athens stock exchange for the

period January 1997 to December 2003.

This period was specifically chosen because it is characterized by intense return volatility. The

period consisted of historically high returns for the Greek Stock market as well as significant

decrease in asset returns. These market return characteristics make it possible to have an

empirical investigation of the pricing models on differing financial conditions thus obtaining

conclusions under varying stock return volatility.

The paper excluded financial firms because of the high leverage that is normal for these firms do

not have the same meaning as for non financial firms, where high leverage is more likely toindicate distress. Shares not included in the sample are either thinly traded or do not have

accounting and financial information on a continuous basis.

Athens composite share index was used as a world portfolio proxy. The world portfolio

represents the total market value of all stocks (or bonds or any financial or non-financial

instruments) that an investor would own if he or she bought the total of all marketable stocks on

all the major stock exchanges.

When choosing a proxy of world stock American market indices such as the S&P500, Dow

Jones Industrial Average (DJIA) or the New York Stock Exchange (NYSE) has been rejected

since reliable financial data show that a typical American investor avoids investing into foreign

financial markets such as Greece.

The estimation of characteristic lines


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The 100 stocks that were used were divided into portfolios according to their size as it was

calculated at the end of June each year (Michailidis et al. 2007:12). Portfolios, rather than

individual stocks, were used to reduce the noisiness of the data in order to diversify away most

of the firm-specific part of returns and mitigate the problems that arise from measurement error

in beta estimates. The first type of evidence is in what APT and CAPM can explain of the

returns used in their estimation. As the single market index factor for the Capital Asset Price

Model, we use the ASE Composite Share Index. To calculate APT ( arbitrage pricing model),

factor scores from the monthly returns we use a multifactor pricing model in order to identify

which factors best capture systematic return co-variation (risk) of the Greek equity returns

(Michailidis et al. 2007:12). The linkages between equity prices and variables such as money

supply, inflation and industrial production are of crucial importance not only in analyzing equity

returns, but also in understanding the connections between expected returns and the real

economy. From the standpoint of both the academic researcher and the investment practitioner,

therefore, it is crucial to be able to identify which factors best capture the systematic components

of stock return variation (Michailidis et al. 2007:12). A central empirical issue, therefore, is which

factors best account for the common movements in returns.

The list of candidates for factors is a long one, so a sensible process of elimination is essential. In

accordance with the rational expectations and market efficiency hypothesis, the innovations inthe macroeconomic series are estimated; the variables included in the return generating process

are then selected on the basis of their ability to predict the factor scores estimated using Factor

Analysis. The approach is to extract the principal components from the data and apply formal

statistical tests to discriminate between the factors (Michailidis et al. 2007:13).

The rule for selecting the variables is based on the eigenvalues that exceeds 1. The values in the

column initial eigenvalues-total indicate the proportion of each variable's variance that can be

explained by the principal components. Variables with values greater than 1 are well represented

in the common factor space, while variables with values less than 1 are not well represented as

shown by the total column of the table 1 below (Michailidis et al. 2007:13).


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Table 1

Initial Eigenvalues

Component Total% of

VarianceCumulative %

OILPR 1.534 25.568 25.568

INDPR 1.234 20.564 46.132

INF 1.071 17.848 63.980

EXRA .848 14.134 78.114

TERSTR .699 11.658 89.772

RISKPR .614 10.228 100.000

In the second column of table (total eigenvalue) we find the variance of the factors that explain

the higher percent of the total variance. As it can be seen factor 1 accounts for 26% of the

variance, factor 2 for 21%, and so on (Michailidis et al. 2007:13). The third column contains the

cumulative variance extracted. For example, the third factor has a cumulative value of 63.98

meaning that the first three components together account for almost 64% of the total variance.So according to the results of the PCA the macroeconomic variables of oil prices, industrial

production and inflation has been selected as the macro-variables for the Arbitrage pricing

model (Michailidis et al. 2007:14).


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Estimates of Expected Returns

For one to be concerned with the CAPMs challenge to the APT, the models must suggest different

policy choices. In the study an estimated CAPM equation for all companies was made for the period

1997 to 2003 using monthly return data and each year a portfolio was then created in accordance

with the portfolio size. To acquire the expected return associated with the varying levels of risk, they

made use of a CAPM equation comprising of the average risk free rate and the average annual

equivalent of the average relationship of return to systematic risk for all stocks on the Athens stock

exchange (ref page 10).


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The Rf represents the risk free rate and the Rm represents the expected return on the market. The

systematic risk and required returns for each portfolio are also calculated and shown above. An

analysis of the calculations made shows that low capitalisation portfolios provide better returns and

less systematic risk is associated with higher returns.

The same calculations were made for the APT. it included all stocks traded on a regular basis on the

Athens Stock exchange between 1997 and 2003. It was made to analyse three sectors and their

various portfolio returns. These included oil prices, industrial production and inflation.


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Conclusion

In the study carried out it was shown that low capitalisation portfolios provided better returns than

those portfolios which comprised of a big size of stocks. Small to medium sized portfolios showed

less systematic risk which led to higher returns for the periods 1997 to 2003. The average mean

values of the CAPM which were worked out for both models indicated that the CAPM would higher

returns than the APT. The APT is clearly an improved version of the CAPM but the use of the CAPM is

still necessary.

The CAPM is still necessary as in practise the APT does not work better than the CAPM. This is

because the APT has estimation errors associated with it. It also does not tell the user how many

factors need to be used and what those factors should be. The CAPM is much simpler and the

estimation of 1 and Rm is much simpler . As advanced as the APT might be its estimation errors

would seem to cancel it out. The required return acquired from it is not as accurate as that of the

CAPM. The APT is much harder to understand and use and is therefore rarely used in the

computation of required returns, but it does have helpful applications in investment management .

Based on evidence gathered the CAPM cannot be rejected in favour of any alternative hypothesis

and performs very well against the APT as shown in the study of the Athens stock exchange. The

CAPM is a reasonable model for explaining cross sectional variations in asset returns. The study can

be seen as a possibly method of solving the problem as to what determines the expected returns of

assets. Two approaches can be taken for this.


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The first of these includes making assumptions and producing a theory that states which variables

should be used in the equation and then testing it. The second of these is the examination of assets

realized returns and determining empirically to which macro variables they correspond. The APT

seems to be more in the spirit of the second. After accessing both models one can draw to the

conclusion that putting one against the other would lead to a situation were you win some on one

hand and lose some on the other hand. Instead of trying to find out which of the two models is

better, one should thoroughly understand their weaknesses and strengths, so that we will know

when and how, which model we can rely on in making financial decisions .

SUMMARY OF THE MAIN CONCLUSIONS:

Two models must suggest different policies Low vs. Big size Stocks

Why still use CAPM? Simple minded but more preciseATP has greater estimation errorsATP difficult to use

Therefore:

Cannot reject CAPM 2 ways to solve problem of Expected Returns on Assets

Win some lose some situation


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YOU TUBE LINK FOR THE VIDEO FOR MORE CLARITY

http://www.youtube.com/watch?v=-0EgQ97whWg

MAIN REFERENCE:

ELTON, E.J., GRUBER, M.J., BROWN, S.J. & GOETZMANN, W.N., 2007. Modern

Portfolio Theory and Investment Analysis. Wiley.

ADDITIONIAL REFERENCES:

DHANKAR, R.S., and SINGH, R., (2005). Arbitrage Pricing Theory and The Capital Asset

Pricing Model Evidence from The Indian Stock Market. Journal of Financial Management and

Analysis, 18 (1): 14-27

MUZIR, E., BULUT,N., and SENGUL, S., (2010). The Prediction Performance of Asset Pricing

Models and Their Capability of Capturing the Effects of Economic Crises: The Case of Istanbul

Stock Exchange. Isletme Arastirmalaria Dergisi. 2 (3): 3-4

HAUGEN, RA., 2000.The secrets of the bag, how to predict results and profit shares.

New York: Pearson Education.

Singh, R. 2008. CAPM vs. APT with macro economic variables: evidence from the Indian stock

market.Asia-Pacific Business Review.

[Online]. Available:

http://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/pg_12/?tag=mantle_skin;co

ntent[Accessed 6 May 2010].
http://www.youtube.com/watch?v=-0EgQ97whWghttp://www.youtube.com/watch?v=-0EgQ97whWghttp://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/http://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/http://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/pg_12/?tag=mantle_skin;contenthttp://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/pg_12/?tag=mantle_skin;contenthttp://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/pg_12/?tag=mantle_skin;contenthttp://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/pg_12/?tag=mantle_skin;contenthttp://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/pg_12/?tag=mantle_skin;contenthttp://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/http://findarticles.com/p/articles/mi_6771/is_1_4/ai_n28532457/http://www.youtube.com/watch?v=-0EgQ97whWg

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Topic 3 Essay APT